Partial Differential Equations and Probability Density Functions
Please see the attached file for the fully formatted problems. 1) Suppose that S is a random variable that is defined on [0,∞) and whose probability density function is: G(s) = , a and b being positive numbers. Show: where N(z) = . 2) We know that the solution of the final value problem , 0 ≤ ...continues
Partial Differential Equations : Wiener Process and Ito's Lemma
Consider a random variable r satisfying the stochastic differential equation: where are positive constants and dX is a Wiener process. Let ξ = , which transforms the domain for r into (-1,1) for ξ. Suppose the stochastic equation for the new random variable ξ is in the form: d ξ = a(ξ) ...continues
Financial Stochastic Partial Differential Equations : Wiener Processes and Ito's Lemma
Suppose that a random variable satisfies , where dX is a Wiener process. Find the stochastic equation for by using Ito’s lemma and determine the mean and variance of .
Financial Partial Differential Equations : Black-Scholes and Ito's Lemma
Please see the attached file for the fully formatted problems. If and we let , then , where and . Define . Suppose that the stock pays dividends continuously: • D(S,t) => dividend • If dividend is paid continuosly: * D(S,t)dt = D0Sdt * D0 is a constant dividend rate Derive the equation for directly by using ...continues
Differential Equations and Slope Fields
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Differential Equations, Voltage and Capacitance
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Differential Equations, Logistic Equations and Slope Fields
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Differential Equation--Euler's Method
From Differential Equations. Material from Numerical Technique: Euler's Method.
Differential Equations, Existence and Uniqueness of Solutions
Differential Equations From Existence and Uniqueness of Solutions
Differential Equations, Equilibria and the Phase Line
Differential Equations From Equilibria and the Phase Line.
